| Schmidt, D.: From trace sets to modal-transition systems by stepwise abstract interpretation. Submitted for publication (2001) |
....The abstraction involved in building the model of the program semantics is usually left implicit and not discussed. The importance of this abstraction appears when it is made explicit for example in order to discuss the soundness and (in)completeness of temporal logic based verification methods [1, 2]. The purpose of this paper is to discuss the practical importance of this abstraction when designing static software checking algorithms. This is illustrated on reachability analysis and abstract testing. 2 Transition Systems We follow [3, 4] in formalizing a hardware or software computer ....
.... (1) for a small step operational semantics xS, t, Iy of the program (or more precisely, abstract model checking since abstract interpretation is involved) Note that with state to state abstraction, the correctness of the formula in the abstract does not imply its correctness in the concrete (see [1, 2]) A simple counter example would be the termination of: n : f : 1; b : true; while ( n 0) b) do f : f n) n : n 1) od; where memory states xn, f, by are abstracted by xn, fy. So the verification of (1) cannot be done with upper approximations only and would also require a ....
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Schmidt, D.: From trace sets to modal-transition systems by stepwise abstract interpretation. Submitted for publication (2001)
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